%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO061^4 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 03:24:48 PM UTC 2025 % Result : Theorem 0.14s 0.39s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : SYO061^4 : TPTP v9.2.0. Released v4.0.0. % 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n022.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 9 00:54:08 EDT 2025 % 0.14/0.36 % CPUTime : % 0.14/0.39 % SZS status Theorem % 0.14/0.39 % Mode: mode213 % 0.14/0.39 % Inferences: 8 % 0.14/0.39 % SZS output start Proof % 0.14/0.39 thf(ty_a, type, a : ($i>$o)). % 0.14/0.39 thf(ty_eigen__1, type, eigen__1 : $i). % 0.14/0.39 thf(ty_b, type, b : ($i>$o)). % 0.14/0.39 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.39 thf(ty_irel, type, irel : ($i>$i>$o)). % 0.14/0.39 thf(sP1,plain,sP1 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.39 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.39 thf(sP3,plain,sP3 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.14/0.39 thf(sP4,plain,sP4 <=> (sP1 => (b @ eigen__1)),introduced(definition,[new_symbols(definition,[sP4])])). % 0.14/0.39 thf(sP5,plain,sP5 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.14/0.39 thf(sP6,plain,sP6 <=> (b @ eigen__1),introduced(definition,[new_symbols(definition,[sP6])])). % 0.14/0.39 thf(sP7,plain,sP7 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.14/0.39 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.14/0.39 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.14/0.39 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.14/0.39 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.14/0.39 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 0.14/0.39 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 0.14/0.39 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 0.14/0.39 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 0.14/0.39 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 0.14/0.39 thf(def_iand,definition,(iand = mand)). % 0.14/0.39 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.14/0.39 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 0.14/0.39 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 0.14/0.39 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 0.14/0.39 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 0.14/0.39 thf(def_ivalid,definition,(ivalid = (!!))). % 0.14/0.39 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.14/0.39 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.14/0.39 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.14/0.39 thf(con,conjecture,(![X1:$i]:((~((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2)))))). % 0.14/0.39 thf(h0,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[con])). % 0.14/0.39 thf(h1,assumption,(~(sP2)),introduced(assumption,[])). % 0.14/0.39 thf(h2,assumption,sP5,introduced(assumption,[])). % 0.14/0.39 thf(h3,assumption,(~(sP3)),introduced(assumption,[])). % 0.14/0.39 thf(h4,assumption,(~(sP4)),introduced(assumption,[])). % 0.14/0.39 thf(h5,assumption,sP1,introduced(assumption,[])). % 0.14/0.39 thf(h6,assumption,(~(sP6)),introduced(assumption,[])). % 0.14/0.39 thf(1,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])). % 0.14/0.39 thf(2,plain,((~(sP4) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.14/0.39 thf(3,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])). % 0.14/0.39 thf(4,plain,((~(sP2) | ~(sP5)) | sP3),inference(prop_rule,[status(thm)],[])). % 0.14/0.39 thf(axiom1,axiom,(ivalid @ ((iimplies @ (iatom @ a)) @ (iatom @ b)))). % 0.14/0.39 thf(5,plain,sP7,inference(preprocess,[status(thm)],[axiom1]). % 0.14/0.39 thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,h2,h5,h6])). % 0.14/0.39 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,6,h5,h6])). % 0.14/0.39 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,7,h4])). % 0.14/0.39 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,8,h2,h3])). % 0.14/0.39 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1])). % 0.14/0.39 thf(0,theorem,(![X1:$i]:((~((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). % 0.14/0.39 % SZS output end Proof %------------------------------------------------------------------------------